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I am not sure of using no and not in case an adjective follows. What is the right one between two examples below?

Period of access providing (not longer than 1 year)

Period of access providing (no longer than 1 year)

The usage of no/not with nouns is clear, but with adjective it is confusing.

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    What do you mean by "period of access providing"? Also are the parentheses part of the sentence? Could you please provide an example of the complete sentence, as this is just a fragment. It would help us better understand the context. – Andrew Dec 6 '18 at 17:30
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If I rephrase your sentence to something like we provide a period of access (no / not) longer than 1 year, then both versions are grammatical.

To me, no longer sounds more natural, while not longer seems more formal. However, that's mostly a personal opinion.

In terms of idiomatic use, Google Books NGram Viewer suggests that no longer is the more common of the two (at least in writing):

(no/not) longer than

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